Consider g in C^1[0,1]. We say that g is nowhere convex (concave, resp.) on [0,1] if there is no open interval I sube[0,1] on which g is convex (concave, resp.) Is it possible to find a function g which satisfies: (strong verison) g is C^2[0,1] and g is nowhere convex and nowhere concave on [0,1]?

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f(x,y)=x^3-6xy+8y^3$

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